Question: Let $h(x)=9\cos(x)-7x^2$. $h'(x)=$
The expression for $h(x)$ includes $\cos(x)$. Remember that the derivative of $\cos(x)$ is $-\sin(x)$. Put another way, $\dfrac{d}{dx}[\cos(x)]=-\sin(x)$. $\begin{aligned} h'(x)&=\dfrac{d}{dx}[9\cos(x)-7x^2] \\\\ &=9\dfrac{d}{dx}[\cos(x)]-7\dfrac{d}{dx}(x^2) \\\\ &=9(-\sin(x))-7\cdot2x \\\\ &=-9\sin(x)-14x \end{aligned}$ In conclusion, $h'(x)=-9\sin(x)-14x$